Displaying similar documents to “Globally regular solutions to the u 5 Klein-Gordon equation”

Breakdown in finite time of solutions to a one-dimensional wave equation.

Mokhtar Kirane, Salim A. Messaoudi (2000)

Revista Matemática Complutense

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We consider a special type of a one-dimensional quasilinear wave equation w - phi (w / w) w = 0 in a bounded domain with Dirichlet boundary conditions and show that classical solutions blow up in finite time even for small initial data in some norm.

Coherent nonlinear waves and the Wiener algebra

Guy Métivier, Jean-Luc Joly, Jeffrey Rauch (1994)

Annales de l'institut Fourier

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We study oscillatory solutions of semilinear first order symmetric hyperbolic system L u = f ( t , x , u , u ‾ ) , with real analytic f . The main advance in this paper is that it treats multidimensional problems with profiles that are almost periodic in T , X with only the natural hypothesis of coherence. In the special case where L has constant coefficients and the phases are linear, the solutions have asymptotic description u ϵ = U ( t , x , t / ϵ , x / ϵ ) + o ( 1 ) where the profile U ( t , x , T , X ) is almost periodic...